Quotations

Correlation coefficients are now about as ubiquitous and unsurprising as cockroaches in New York City.

In Stephen Jay Gould's The Mismeasure of Man, Second edition, 1996, Page 286.

Forsooths

Growing up in China [Yale Assistant Professor of Genetics] Jun Lu might have pursued a career in math if his father, a mathematician, hadn't advised against it.

His reasoning: Math can be done with little more than a pen, paper and your mind. For 2,000 years, thinkers have had those tools to contemplate the questions of mathematics. "Any questions left behind by them are probably very hard to address," Lu said.

But biology, his father said, capitalized on advances in technology. His son could have the chance to explore a new frontier.

A University of California at Riverside study, published in Social Psychiatry & Psychiatric Epidemiology, found, surprisingly, that suicides are more likely to occur on Wednesdays than on any other day of the week. The study’s results were based on the 131,636 suicides in U.S. death records for the period 2000-2004.

One chart [1] gives the percentages of all U.S. adult suicides by day of the week: Sunday 11.8%; Monday 14.3%; Tuesday 12.7%; Wednesday 24.6%; Thursday 11.1%; Friday 11.2%; Saturday 14.4%.

A social worker suggested that workplace stress might mount up through the week, with weekend relief seeming too far away by Wednesday. A reader [2] blogged that a person in crisis might be upset to find that his/her therapist has Wednesday off, while he/she has to work. One of the researchers advised mental health workers to schedule more patient appointments on Wednesdays.

The researchers also found that summer and spring were more common seasons for suicide than fall or winter, another counterintuitive finding. A second chart [3] gives the percentages of all U.S. adult suicides by season: Autumn 23.8%; Winter 24.4%; Spring 25.8%; Summer 26%.

A third chart [4] shows the trend in the number of U.S. adult suicides (eyeballed approximations): 24,200 in Year 2000; 25,100 in Year 2001; 29,000 in Year 2002; 26,100 in Year 2003; 26,900 in Year 2004.

A Hartford Courant analysis of the 966 reported adult suicides in Connecticut for the period 2001-2004 showed less variation in rates among the days of the week. “Most suicides – 16.7 percent — occurred on Tuesday, while 16.4 percent occurred on Monday and 14.5 percent on Wednesday. Thursday had the lowest occurrence, 12.1 percent.”

However, Connecticut records agreed with the national study with respect to summer and spring being the more common seasons for suicides. A Connecticut mental health worker hypothesized that:

“People think it’s normal to be depressed in the winter. “Spring is the time of year when people are supposed to be rejuvenated and outside and enjoying themselves, and if you’re not, it makes you feel comparatively worse than everybody else, which may make you feel more hopeless,” he said.

Discussion

1. With respect to the national study, do you think that the differences among days of the week and/or among seasons of the year were statistically significant?

2. Were you surprised that the Connecticut analysis showed less variation than the national study, in rates among the days of the week, from a statistical point of view?

Two new anti-aging studies

In the journal Nature, anti-aging researchers from Maine, Michigan, and Texas reported on a study that found that a chemical (Wyeth’s rapamycin) used to treat organ transplant patients increased the life span of mice. Because the chemical suppresses the immune system, humans are advised against taking the drug to prolong their lives.

Mice given rapamycin -- starting when they were 600 days old, or roughly the equivalent of 60 human years -- lived longer on average than mice who didn't get the drug. Their "maximal life span" -- meaning the age at which 10% of the mice were still alive -- increased to 1,245 days for females, compared with 1,094 days for those not fed the drug, or a 14% increase. For males, the maximal life span was 1,179 days, a 9% increase over the 1,078 days for those not fed the drug.

In an upcoming issue of Science magazine, University of Wisconsin scientists will publish results of a study that shows that reducing the calorie intake of monkeys extends their lives. A person who has seen the study's results said that "after 20 years, only 20% of the calorie-restricted monkeys had died, compared with half of the monkeys on a normal diet."

The Wisconsin study, which began in 1989 with 30 monkeys and added 46 more in 1994, is an effort to test calorie restriction in an animal genetically closer to humans. Researchers have known since the 1930s that eating 30% fewer calories than normal lengthens the life span of mice. Half the monkeys were given a normal diet, and half had their food intake cut back by 30% at roughly age 10.

A British gerontologist commented, "Aging is, unequivocally, the major cause of death in the industrialized world and a perfectly legitimate target of medical intervention."

A blogger [5] provided the following hypothetical dialogue.
Joe: Do you want to live to 100?
Pete: Don't ask me; ask the guy who's 99.

Joltin’ Joe

This article discusses “streaks,” especially the 56 consecutive baseball games in which Joe DiMaggio had at least one hit, and people’s intuitions about them. The author [6] is a Caltech professor, who wrote The Drunkard’s Walk: How Randomness Rules Our Lives.

[R]andom processes do display periods of order. In a toss of 100 coins, for example, the chances are more than 75% that you will see a streak of six or more heads or tails, and almost 10% that you’ll produce a streak of 10 or more. As a result a streak can look quite impressive even if it is due to nothing more than chance.
A few years ago Bill Miller of the Legg Mason Value Trust Fund was the most celebrated fund manager on Wall Street because his fund outperformed the broad market for 15 years straight. It was a feat compared regularly to DiMaggio’s, but if all the comparable fund managers over the past 40 years had been doing nothing but flipping coins, the chances are 75% that one of them would have matched or exceeded Mr. Miller’s streak.

The author argues that DiMaggio’s streak could have occurred by chance alone, based on DiMaggio’s lifetime batting average of 0.325, and the fact that hundreds of players had been trying for such a streak over a hundred years.

The author points out that there are many factors involved in analyzing baseball streaks, e.g., variations in batting averages over time. Samuel Arbesman and Stephen H. Strogatz, of Cornell, carried out a 10,000-case computer simulation based on baseball players’ actual statistics from each year 1871-2005. They found that streaks ranged from 39 games to 109 games, with 42% having streaks of DiMaggio’s length or longer.

In discussing people’s misconceptions about streaks, the author cites Thomas Gilovich, Robert Vallone, and Amos Tversky’s paper, “The Hot Hand in Basketball: On the Misperception of Random Sequences.” [7]
Other well known resources not cited in this article include Thomas Gilovich’s 1998 Chance video “Streaks in Sports” [8], and Stephen Jay Gould’s 1988 book review “The Streak of Streaks” [9].

(a) Strogatz's simulation had Cobb out-hitting DiMaggio 300 out of 10000 times, or 3%. Dunno how long he played, but much longer than 3% of baseball. 10000 "seasons" is a sample 100 times greater than reality.

(b) …. “Don’t give me brilliant generals; give me lucky generals.” –Caesar. …. As a former baseball player, I know how hard it is to get a hit on those days when you're just not feeling it. I don't think coins have those days ....

Discussion

1. In a toss of 100 coins, what is the probability of seeing a streak of 6 or more heads? Here [11] is a website with an applet calculator and an explanation of the reasoning behind the calculations.

2. Show that, in a toss of 100 coins, the probability of seeing a streak of 6 or more heads or tails is more than 75%.

Confidence intervals as public policy

Note: This PBS program may be two years old; nevertheless, it has provided the contributor with good class discussion.

This round table program about the 2002 No Child Left Behind (NCLB) Act covered two important aspects of the national assessment of student progress mandated by this act:
(1) Each state has the discretion to set its own passing percentages and must raise its bars annually;
(2) States may use a confidence interval centered about a subgroup's passing percentage and deem that subgroup's progress successful if the confidence interval "captures” the target passing percentage, as long as a subgroup meets a minimum state-determined size.

Merrow contrasted this assessment-of-progress system to 100-meter hurdle events, in which “all the hurdles are the same height.” He stated that 9 states set the early NCLB bars “very close to the ground,” in order to show more progress toward what Finn called the unrealistic national goal of 100 percent proficiency by 2014.

Merrow noted that, unlike hurdle events, states are evaluated by how well traditionally underserved groups of students progress. However, if a subgroup does not meet its minimum size requirement, results are not reported for that subgroup. Finn estimated that about 2 million minority students are not counted because, as subgroups in various municipalities, their size does not warrant reporting. With the Department of Education’s approval, states can increase their minimum subgroup size and avoid having to report a group’s progress.

Merrow described how schools, unlike athletic event judges, may use confidence intervals to “capture” a passing percentage for a subgroup, and Carey claims that some margins of error are as large as 30 points.

JOHN MERROW: So if my school scored 30 and passing is 55, but the confidence interval [radius] is 30 points, we can say we passed?

KEVIN CAREY: Yes.

JOHN MERROW: Nearly all states use confidence intervals. In Illinois, 509 schools were saved from failing because confidence intervals added up to 12 points to their scores.

Carey felt that percent-passing scores measured in this way gave the public a false impression of the performance of their students. Spellings defended the Act as the beginning of educational accountability, flawed as it may be, and she foresaw future adjustments to the requirements.

We have to ensure that we are as accurate as we can be, …. That’s the reason we’re using a 99% confidence interval as opposed to a 95% confidence interval.

A mathematics professor at the University of Wisconsin-Milwaukee stated,

The charitable way to view this is to say they chose 99% to make sure that anybody who they said was bad, really, really is bad …. The uncharitable way to view this is to say they chose 99% so they would have to say as few people are bad as possible.

Another Wisconsin statistician feels that the use of confidence intervals “appears to be reasonable, given the consequences of being flagged as a school failing to make progress.”

Discussion

1. (Contributor will provide questions about appropriateness of confidence intervals in this context - what do they tell you, do you have the required conditions, etc., from her class notes.) or (Other contributors are welcome to chime in.)

THE FLAW OF AVERAGES

Sam L. Savage
John Wiley & Sons, published June 2009.

This is a fascinating book and I will review it here but with the slowness that comes with old age. However this old allows me fond memories of Sam's father, I Richard Savage. In his Memorial we read]:

Savage is one of a few mathematical statisticians of his generation who chose to pursue the application of statistical principles and concepts to problems of public policy.

Now his son is one of the few mathematical probabilist who chooses to pursue the application of probability to problems of public interest.